Whether you can break into the industry kind of depends on where you live and what opportunities are in your area. Since you are just wanting a taste you can always apply to be an extra.
Here in L.A. there is a company called Central Casting that is the "go to" agency for extras. You can go there and apply to be an extra; they will take your stats and will take pictures of you. Prospective clients look through books of people that have applied to be extras and who meet the general look that the client wants, and the client will select the candidates they are interested in. Whether or not you ever get picked is a crap shoot.
I applied and I got a call within a week and that led to working as an extra on a shoot for a commercial at the Warner brothers lot. I've had two calls since then but was unable to accept the work due to other commitments. All of this has happened since last July.
Good luck!